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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Editor: Stephen A. Burns
  • Vol. 25, Iss. 7 — Jul. 1, 2008
  • pp: 1772–1782

Accurate image reconstruction from few-view and limited-angle data in diffraction tomography

Samuel J. LaRoque, Emil Y. Sidky, and Xiaochuan Pan  »View Author Affiliations


JOSA A, Vol. 25, Issue 7, pp. 1772-1782 (2008)
http://dx.doi.org/10.1364/JOSAA.25.001772


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Abstract

We present a method for obtaining accurate image reconstruction from highly sparse data in diffraction tomography (DT). A practical need exists for reconstruction from few-view and limited-angle data, as this can greatly reduce required scan times in DT. Our method does this by minimizing the total variation (TV) of the estimated image, subject to the constraint that the Fourier transform of the estimated image matches the measured Fourier data samples. Using simulation studies, we show that the TV-minimization algorithm allows accurate reconstruction in a variety of few-view and limited-angle situations in DT. Accurate image reconstruction is obtained from far fewer data samples than are required by common algorithms such as the filtered-backpropagation algorithm. Overall our results indicate that the TV-minimization algorithm can be successfully applied to DT image reconstruction under a variety of scan configurations and data conditions of practical significance.

© 2008 Optical Society of America

OCIS Codes
(170.3880) Medical optics and biotechnology : Medical and biological imaging
(110.6955) Imaging systems : Tomographic imaging
(110.3010) Imaging systems : Image reconstruction techniques

ToC Category:
Imaging Systems

History
Original Manuscript: August 6, 2007
Revised Manuscript: April 8, 2008
Manuscript Accepted: May 4, 2008
Published: June 26, 2008

Virtual Issues
Vol. 3, Iss. 8 Virtual Journal for Biomedical Optics

Citation
Samuel J. LaRoque, Emil Y. Sidky, and Xiaochuan Pan, "Accurate image reconstruction from few-view and limited-angle data in diffraction tomography," J. Opt. Soc. Am. A 25, 1772-1782 (2008)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-25-7-1772


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References

  1. M. Slaney and A. C. Kak, “Diffraction tomography,” in Inverse Optics, Vol. 14, A.J.Devaney, ed. (SPIE, 1983), pp. 2-19.
  2. M. P. Andre, P. J. Martin, G. P. Otto, L. K. Olson, T. K. Barrett, B. A. Spivey, and D. A. Palmer, “A new consideration of diffraction computed tomography for breast imaging: Studies in phantoms and patients,” Acoust. Imaging 21, 379-390 (1995).
  3. A. Devaney, “Geophysical diffraction tomography,” IEEE Trans. Geosci. Remote Sens. 22, 3-13 (1984). [CrossRef]
  4. V. E. Kunitsyn, E. S. Andreeva, E. D. Tereschenko, B. Z. Khudukon, and T. Nygren, “Investigations of the ionosphere by satellite radiotomography,” Int. J. Imaging Syst. Technol. 5, 112-127 (1994). [CrossRef]
  5. R. Mueller, M. Kaveh, and G. Wade, “Reconstructive tomography and applications to ultrasonics,” in Proc. IEEE 67, 567-587 (1979). [CrossRef]
  6. S. X. Pan and A. C. Kak, “A computational study of reconstruction algorithms for diffraction tomography: Interpolation versus filtered backpropagation,” IEEE Trans. Acoust., Speech, Signal Process. 31, 1262-1275 (1983). [CrossRef]
  7. A. Devaney, “A filtered backpropagation algorithm for diffraction tomography,” Ultrason. Imaging 4, 336-350 (1982). [CrossRef] [PubMed]
  8. P. Guo and A. J. Devaney, “Comparison of reconstruction algorithms for optical diffraction tomography,” J. Opt. Soc. Am. A 22, 2338-2347 (2005). [CrossRef]
  9. E. Candes, J. Romberg, and T. Tao, “Robust uncertainty principles: Exact signal reconstruction from highly incomplete frequency information,” IEEE Trans. Inf. Theory 52, 489-509 (2006). [CrossRef]
  10. E. Y. Sidky, C. Kao, and X. Pan, “Accurate image reconstruction from few-views and limited-angle data in divergent-beam CT,” J. X-Ray Sci. Technol. 14, 1-21 (2006).
  11. E. Wolf, “Three-dimensional structure determination of semi-transparent objects from holographic data,” Opt. Commun. 1, 153-156 (1969). [CrossRef]
  12. X. Pan, “Unified reconstruction theory for diffraction tomography, with consideration of noise control,” J. Opt. Soc. Am. A 15, 2312-2326 (1998). [CrossRef]
  13. A. C. Kak and M. Slaney, Principles of Computerized Tomographic Imaging (SIAM, 2001). [CrossRef]
  14. X. Pan and M. A. Anastasio, “Minimal-scan filtered backpropagation algorithms for diffraction tomography,” J. Opt. Soc. Am. A 16, 2896-2903 (1999). [CrossRef]
  15. M. H. Li, H. Q. Yang, and H. Kudo, “An accurate iterative reconstruction algorithm for sparse objects: Application to 3D blood vessel reconstruction from a limited number of projections,” Phys. Med. Biol. 47, 2599-2609 (2002). [CrossRef] [PubMed]
  16. E. Candes and T. Tao, “Near optimal signal recovery from random projections: Universal encoding strategies,” IEEE Trans. Inf. Theory 52, 5406-5425 (2004). [CrossRef]
  17. E. Y. Sidky, University of Chicago, Department of Radiology, 5841 S. Maryland Ave. MC2026, Chicago, Illinois 60637, USA, and X. Pan are preparing a manuscript to be called “Image reconstruction in circular cone-beam computed tomography by total variation minimization.”

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